Minimum Coin Change Problem

How to solve Minimum Coin Change Problem using bottom up dp?

You can refer this video. It clearly explain each and every step of this question.

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For bottom up solution, you can start filling the values from 0 and then maintaining a dp table fill the values for all the values upto n.

for (i = 1; i < n+1; i++)
    for (j = 0; j < m; j++)
        // Count of solutions including S[j]
        x = (i-S[j] >= 0)? table[i - S[j]][j]: 0;

        // Count of solutions excluding S[j]
        y = (j >= 1)? table[i][j-1]: 0;

        // total count
        table[i][j] = min(x,y);

For more explanation check the GeeksForGeeks Solution. Please note Geeks For Geeks Solution is for total no of ways, for minimum coins just replace x+y with min(x,y).

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I want to the minimum numbers of coins to fulfill amount .

table[i][j] = min(x,y), will give you the minimum amount to fulfil amount i using coins upto value S[j].
So table[n][m-1] will give you minimum amount to fulfill n using coins upto S[m-1] i.e. all the coins.

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